Moduli selection is one of the most important issues in the implementation of systems that make use of residue number systems. In this paper, we describe a software tool that assists system designers in moduli selection for the design of RNS-based FIR filters and filter banks. According to some filter specification parameters, the software tool constructs valid moduli sets and calculates their ...

In this paper, we propose the new moduli set { − , , + } with an efficient reverse converter. Experiments were performed on our converter and the state of the art using Xilinx ISE 14.3 software to target a Spartan 3 FPGA board. The results from these experiments suggest that on the average, the proposed converter outperforms the state of the art converters for the moduli sets { − , , + } and { ...

The affine Grassmannian is an important object that comes up when one studies moduli spaces of the form BunG(X), where X is an algebraic curve and G is an algebraic group. There is a sense in which it describes the local geometry of such moduli spaces. I’ll describe the affine Grassmannian as a moduli space, and construct it concretely for some concrete groups. References, including the constru...

In this paper we introduce a new algorithm for division in residue number system, which can be applied to any moduli set. Simulation results indicated that the algorithm is faster than the most competitive published work. To further improve this speed, we customize this algorithm to serve two specific moduli sets: (2k, 2k −1, 2k−1 −1) and (2k +1, 2k, 2k −1). The customization results in elimina...

For a perfect field k, we study actions of the absolute Galois group of k on the k-valued points of moduli spaces of quiver representations over k; the fixed locus is the set of k-rational points and we obtain a decomposition of this fixed locus indexed by elements in the Brauer group of k. We provide a modular interpretation of this decomposition using quiver representations over division alge...

In our previous paper [18], we introduced the tautological rings of the genus zero moduli spaces of stable maps to homogeneous spaces X. We showed that in the case of SL flags, all rational cohomology classes on the stable map spaces are tautological using methods from Hodge theory. The purpose of this note is to indicate a localization proof, in the spirit of Gromov-Witten theory, when X is a ...

We show that the skeleton of the Deligne-MumfordKnudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the “naive” set-theoretic tropicalization map. The proof passes through general structure results on the skeleton of a toroidal Deligne-Mumford stack. Furthermore, we construct tautological forgetful, cl...

We study matrix string scattering amplitudes and matrix string instantons on a marked Riemann surface in the limit of a vanishing string coupling constant. We give an explicit parameterization of the moduli space of such instantons. We also give a description of the set of fermionic supermoduli. The integration over the supermoduli leads to the inclusion of picture changing operators at the int...

The paper discusses the problem of manufacturability of the minimum compliance designs of the structural elements made of two kinds of inhomogeneous materials: the isotropic and cubic. In both the cases the unit cost of the design is assumed as equal to the trace of the Hooke tensor. The Isotropic Material Design (IMD) delivers the optimal distribution of the bulk and shear moduli within the de...